Bug in prox of l1 norm

[mehrhardt]

This example shows a bug in the prox operator of the l1 norm:

import odl

X = odl.rn(1)
f = odl.solvers.L1Norm(X)
x = 0.1 * X.one()

y1 = x.copy()
f.convex_conj.proximal(3)(y1, out=y1)

y2 = x.copy()
y2 = f.convex_conj.proximal(1)(y2)

(y1-y2).norm()

results in 0.9. Similar effects can be observed in KullbackLeibler but not in L2Norm.

[adler-j]

What would be the expected result and why?

Edit: I'm stupid, ofc it should be zero.

[mehrhardt]

As mentioned above already, replacing f by f = odl.solvers.KullbackLeibler(X) yields similar issues. Who knows which other functionals have the same problem.

[adler-j]

Darn it, you are right. I'll look into it.

[mehrhardt]

Any news here? Is there a way to write a test that gets run on all functionals (without us writing a new one every time)?

[adler-j]

No update sadly, havn't had time. With that said there is a rather enormous large-scale test here:

odl/odl/test/largescale/solvers/nonsmooth/default_functionals_slow_test.py

Line 114 in baecb8a

def test_proximal_defintion(functional, stepsize):

it should catch stuff like this, but apparently does not.

[kohr-h]

No update sadly, havn't had time. With that said there is a rather enormous large-scale test here:

odl/odl/test/largescale/solvers/nonsmooth/default_functionals_slow_test.py

Line 114 in baecb8a
def test_proximal_defintion(functional, stepsize):

it should catch stuff like this, but apparently does not.

Does it test with aligned input & output?

[adler-j]

Does it test with aligned input & output?

Very much looks like it does not.

[mehrhardt]

Well done! This indeed fixed the bug I was observing.

[mehrhardt]

I just did a similar test with the l1-norm itself and not its conjugate. While the latter is indeed fixed, the former still has the same problem:

import odl

X = odl.rn(1)
f = odl.solvers.L1Norm(X)
x = 0.1 * X.one()

y1 = x.copy()
f.proximal(1e-2)(y1, out=y1)

y2 = x.copy()
y2 = f.proximal(1e-2)(y2)

(y1-y2).norm()

@adler-j , @kohr-h , any chance this can be fixed easily?